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Magnitude condition
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Magnitude condition : ウィキペディア英語版
Magnitude condition


The magnitude condition is a constraint that is satisfied by the locus of points in the s-plane on which closed-loop poles of a system reside. In combination with the angle condition, these two mathematical expressions fully determine the root locus.
Let the characteristic equation of a system be 1+\textbf(s)=0, where \textbf(s)=\frac. Rewriting the equation in polar form is useful.
e^+\textbf(s)=0
\textbf(s)=-1=e^ where
(k=0,1,2,...) are the only solutions to this equation. Rewriting \textbf(s) in factored form,
\textbf(s)=\frac=K\frac,
and representing each factor (s-a_p) and (s-b_q) by their vector equivalents, A_pe^ and B_qe^, respectively, \textbf(s) may be rewritten.
\textbf(s)=K\frac}
Simplifying the characteristic equation,
e^=K\frac}=K\frace^,
from which we derive the magnitude condition:
1=K\frac.
The angle condition is derived similarly.


抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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